摘要
开关磁阻电机由于结构简单、系统可靠性高、对运行环境适用能力强等特点,在很多领域有着广泛的应用,也成为国家863电动汽车项目汽车驱动系统的备选电机之一。本文针对开关磁阻电机研究中的热点和难点问题进行了深入的研究和探讨。
开关磁阻电机稳态及动态运行性能的分析研究。开关磁阻电机虽然结构简单,但由于双凸极的结构特点及控制电路的开关性,电磁关系十分复杂,是一种具有局部高饱和、相间耦合较强的复杂非线性系统,采用常规方法难以准确分析其性能。本文首先针对电机三维磁场分析中的难点问题——三维磁链的计算,提出了结合网格重构思想的计算三维磁链的方法,计算了反映端部磁场随转子位置角及相电流变化的开关磁阻电机绕组端部电感曲线族。
建立了电机磁场方程与主控制电路方程直接耦合的二维场—路—运动耦合有限元模型,分析了不同转速、不同控制方式下电机的稳态运行性能,模拟了电机某一绕组断路的故障运行状态。将端部电感引入二维有限元模型,分析了不同结构及绕组连接方式的开关磁阻电机端部磁场效应的影响。
结合磁场分析,本文提出了根据磁场分布划分铁心区域计算电机铁心损耗的方法,计算并测量了不同转速下电机稳态运行时的铁心损耗。对于电磁系统和机械系统耦合的电机动态性能分析问题,本文建立了电磁方程与机械方程间接耦合的时步有限元模型,分析了开关磁阻电机的起动特性。
电磁力有限元分析方法的研究与应用。深入研究了三种电磁力的计算方法,即麦克斯韦应力法、虚位移法和节点力法,通过理论推导和数值计算给出了二维电磁力有限元分析中麦克斯韦应力法积分路径的选取方法,利用节点力法能够进行局部力分析的特点,通过数值计算分析了开关磁阻电机转子转动过程中定子磁极与转子磁极之间作用力的变化,同时,对节点力法做了进一步的简化,减小了刚性物体全局力分析的计算量。
控制参数对开关磁阻电机振动影响的研究。开关磁阻电机的振动和噪声问题较为突出,对引起振动的两大主要因素——转矩脉动和径向磁拉力的定量分析和研究将为开关磁阻电机振动抑制的研究提供理论基础和研究平台。本文通过数值计算定量分析了开关磁阻电机运行在同一稳态工作点的不同开通、关断角下的转
Switched reluctance motor (SRM) has been used in many fields in view of its applicability in hard operating environments, high reliability and simple structure. Therefore, SRM has been a choice of driving motor for electric automobile in 863 project of our country. The hot and difficult problems in SRM field have been researched in this thesis.SRM steady-state and dynamic-state performance analysis. The electromagnetic field of SRM is very complicated due to its peculiar double salient configuration and switched controlling circuit although its structure is simple. The SRM is such a kind of complex nonlinear system with local high saturation level, not ignorable couple between phases and flexible control that it is difficult to analyze its performance accurately using conventional method. Firstly, for the computation of 3D flux linkage which is a difficult problem in 3D magnetic field analysis of motors, a computing method combined with mesh reconstruction has been proposed based on 3D FEM analysis. The magnetic field of the end-part of SRM varied with rotor position and phases currents have been analyzed, and the inductance curves of the end part of the windings are obtained.A 2D filed-circuit-motion coupled model that magnetic field FEM equations and controlling circuit equations are coupled directly has been presented to calculate the steady-state performance of SRM under different rotating speed and different controlling mode. And the fault operating state that one of the stator windings breaks from the circuit has been simulated using this model. Introducing the inductances of the winding end parts into the 2D FEM model, the effects of end-part magnetic field for SRM with different configuration and different winding connecting type have been investigated in this thesis.A method of predicting iron core losses in SRM has been presented based on electromagnetic field analysis, in which the iron core losses is estimated by series of components and corresponding frequencies of flux densities in different parts of its iron core. The iron core losses of the SRM operating at different rotating speed are estimated and measured. Concerning the dynamic-state performance analysis involving coupled problem between electromagnetic and mechanical system, the time-stepping FEM model is established to predict the starting characteristics of the SRM.Research and application of force calculating methods. Maxwell stress tensor method, virtual work method and nodal force method have been researched and discussed, and the method to choose a proper integrating path in 2D Maxwell stress method is proposed upon theoretical and numerical demonstration. Furthermore, the variation of the force acting among stator and rotor poles of SRM with rotor rotation has been analyzed using the nodal force method, and the nodal force method has been simplified to decrease computation cost with the same accuracy.Influence of controlling parameters on vibration of SRM. The vibration and noise
problem of the SRM is more serious than other motors, which is caused by two main factors, the torque ripple and the radial force acting on stator poles. Therefore, analyzing these two factors quantitatively is significant to decrease the vibration of SRM. The torque ripple and the radial force of SRM on the same steady-state operating point but different switch-on and switch-off angles have been computed numerically in this thesis, and the corresponding vibration waveforms and spectrums for different controlling angles have been tested respectively. Based on these researches, the influence of switch-on and switch-off angle on SRM vibration has been investigated through the analysis of torque ripple and radial force.
引文
[1] 陈清泉,电动汽车——清洁有效的城市交通工具,电工技术杂志,1999(3):5-8
[2] 乔维高,电动汽车的应用及发展,重型汽车,2002(3):13-15
[3] 章超,易家玉,全球电动汽车发展迅猛,电气化,2000(9):14-15
[4] 谭建成,电动汽车及其电驱动技术,电机电器技术,1998(1):19-24
[5] 谭建成,电动汽车及其电驱动技术,电机电器技术,1998(2):16-18
[6] 王怡,胡元德,王义发等,国外电动汽车电机驱动系统发展评述,微电机,1997,30(3):22-27
[7] 孙立志,赵辉,陆永平,电动汽车中的电机驱动系统,电工电能新技术,1997(4):14-19
[8] 詹琼华,开关磁阻电动机,武汉:华中理工大学出版社,1992
[9] 吴建华,开关磁阻电机设计与应用,北京:机械工业出版社,2000
[10] 吴建华,詹琼华,电动车的新型驱动系统—高效节能的开关磁阻电机驱动系统,汽车电器,1995(5):1-4
[11] 刘华,开关磁阻电动机和电动汽车用电动机,电机技术,1997(3):43-49
[12] 樊晓明,朱学忠,刘迪吉,电动车驱动用开关磁阻电机的研究与实践,中小型电机,1997,24(2):21-32
[13] 曹家勇,陈幼平,詹琼华等,开关磁阻电动机控制技术的研究现状和发展趋势,电机与控制学报,2002,6(1):1-5
[14] 詹琼华,马志源,郭伟,电动汽车用20kW开关磁阻电动机的设计与试验研究,电机与控制学报,1999,3(3):161-164
[15] 马莉,陈国林,开关磁阻电机开发应用和函待解决的问题,山西煤炭,1997,17(6):49-51
[16] 贾好来,SRM调速系统技术的研究热点,电工技术,2001(4):4-5
[17] 李俊卿,李和明,开关磁阻电机发展综述,华北电力大学学报,2002,29(1):1-5
[18] P.J.Lawrenson, J.M.Stephenson, P.T.Blenkinsop, Variable-speed switched reluctance motors, IEEE Proc., 1980, 127(4): 253-265
[19] 吴建华,詹琼华,林金铭,开关磁阻电机的前期设计,电工技术学报,1995(1):34-38
[20] 詹琼华,吴莹,郭伟,开关磁阻电机绕组连接方式的研究,电机与控制学报,2002,6(2):93-95
[21] 邱亦慧,马志源,詹琼华,无位置传感器开关磁阻电机的无反转起动研究,电工技术学报,2001,16(2):18-22
[22] 郭伟,詹琼华,丘亦慧,一种新型两相励磁开关磁阻电机驱动系统的静态特性,中国电机工程学报,2002,22(12):91-96
[23] 王宏华,许华,开关型磁阻电动机调速系统的发展及现状,电气传动,2001(5):3-8
[24] 任套牢,卢正雄,孟建新,开关磁阻电机的原理及其应用,煤矿自动化,1998,7(6):8-10
[25] 刘闯,朱学忠,刘迪吉,开关磁阻电机的非线性电感参数法仿真分析,东南大学学报(自然科学版),2001,31(4):106-110
[26] 李少非,开关磁阻电机最小电感解析算法的精确化改进,微电机,2001,34(3):17-18
[27] 孙丹,贺益康,适合与控制策略研究的开关磁阻电机非线性电感模型,微特电机,2001(3):3-5
[28] 徐国卿,郝容泰,开关磁阻电机快速非线性建模方法的研究,北方交通大学学报,1997,21(1):70-73
[29] Stephenson J.M., Corda J., Computation of torque and current on double Salient reluctance motors with nonlinear magnetisation data, IEE Proc., 1979: 393-396
[30] Miller T.J.E., Nonlinear theory of the switched reluctance motor for rapid computer-aided design, IEE Proc., 1990: 337-347
[31] R.Arumugam, D.A.Lowther, J.F.Lindsay, Magnetic Field Analysis of A Switched Reluctance Motor Using A Two Dimensional Finite Element Model, IEEE Trans. on Magnetics, 1985, Mag-21(5): 1883-1885
[32] A.A.Arkadan, B.W.Kielgas, Switched reluctance motor drive systems dynamic performance prediction and experimental verification,IEEE Trans on Energy Conversion, 1994, 9(1): 36-44
[33] A.A.Arkadan, B.W.Kielgas, Switched reluctance motor drive systems dynamic performance prediction under internal and external fault conditions, IEEE Trans. on Energy Conversion, 1994, 9(1): 45-52
[34] A.A.Arkadan, N.A.Demerdash, J.G.Vaidya, M.J.Shah, Impact of Load on Winding Inductances of Permanent Magnet Generators with Multiple Damping Circuits Using Energy Perturbation, Transactions on Energy Conversion, 1988, 3(4): 880-889
[35] A.A.Arkadan, T.M.Hijazi, N.A.Demerdash, J.G.Vaidya, V.K.Maddali, Theoretical Development and Experimental Verification of A DC-AC Electronically Rectified Load-Generator System Model Compatible with Common Network Analysis Software Packages, IEEE Trans. on Energy Conversion, 1988, 3(1): 123-131
[36] A.A.Arkadan, R.Vyas, J.G.Vaidya, M.J.Shah, Effect of Toothless Stator Design on Core and Stator Conductors Eddy Current Losses in Permanent Magnet Generators, IEEE Trans. on Energy Conversion, 1992, 7(1): 231-237
[37] J. Corda, S. Masic, J.M. Stephenson, Computation and experimental determination of running torque waveforms in switched-reluctance motors, IEE Proc., 1993, 140(6): 387-392
[38] N.A. Demerdash, P. Baldassari, A combined finite element-state space modeling environment for induction motors in the ABC frame of reference: the no-load condition, IEEE Trans. on Energy Conversion, 1992, 7(4): 698-708
[39] Nehl T.W., Fouad F.A., Demerdash, Determination of Saturated Values of Rotating Machinery Incremental and Apparent Inductances by An Energy Perturbation Method, IEEE Trans. on Power Appratus and Systems, 1982,PAS-01: 4441-4451
[40] Demerdash N.A., Fouad F.A., Nehl, er, Demerdash N.A., Determination of Winding Inductances in Ferrite Type Permanent Magnet Electric Mathinery by Finite Elements, IEEE Trans. on Magnetics, 1982,Mag-18: 1052-1054
[41] Gwan-Sik Kong, Jin-woo Ahn, Predicting the torque characteristics of switched reluctance motor by using nonlinear inductance profiles, IEEE TENCON 1993: 580-584
[42] R.Wang, N.A.Demerdash, Extra High Speed Modified Lundell Alternator Parameters and Open/Short-Circuit Characteristics From Global 3D-FE Magnetic Field Solutions, IEEE Trans. on Energy Conversion, 1992, 7(2): 330-341
[43] 童怀,傅光洁,黄声华,詹琼华,开关磁阻电机稳态特性的等效磁网络模型分析方法(Ⅰ 数学模型),中国电机工程学报,1998,18(2):106-110
[44] 童怀,傅光洁,黄声华,詹琼华,开关磁阻电机稳态特性的等效磁网络模型分析方法(Ⅱ 系统仿真),中国电机工程学报,1998,18(3):204-207
[45] 童怀,开关磁阻电机等效网络模型的降阶处理方案,电工技术学报,2000,15(1):30-35
[46] Longya Xu, Eric Ruckstadter, Direct Modeling of Swichted Reluctance Machine by Coupled Field-Circuit Method, IEEE Trans. on Energy Conversion, 1995, 10(3): 446-454
[47] 常国强,詹琼华,边敦新,开关磁阻电机驱动系统场路直接耦合的数学模型,中国电机工程学报,2001,21(3):70-73
[48] B.Fahimi, G..Suresh, J.Mahdavi, M.Ehsani, A New Approach to Model Switched Reluctance Motor Drive Application to Dynamic Performance Prediction, Control and Design, PESC 1998: 2097-2102
[49] J.Mahdavi, G.Suresh, B.Fahimi, M.Ehsani, Dynamic Modeling of Nonlinear SRM Drive with Pspice, IEEE Industry Application Society Annual Meeting, 1997, 10: 661-667
[50] K.N. Srinivas, R. Arumugam, Dynamic characterization of switched reluctance motor by computer-aided design and electromagnetic transient simulation, IEEE Trans. on Mags., 2003, 39(3): 1806-1812
[51] Phop Chancharoensook, Muhammed F Rahman, Dynamic Modeling of a Four-Phase 8/6 Switched Reluctance Motor Using Current and Torque Look-Up Tables, IECON 2002: 491-496
[52] F.Soares, P.J.Costa Branco, Simulation of a 6/4 Switched Reluctance Motor Based on Matlab/Simulink Environment, IEEE Trans. on Aerospace and Electronic System, 2001,37(3): 989-1009
[53] 杨仕友,多段圆弧极靴水轮发电机极弧优化、参数计算和动态性能研究,沈阳工业大学博士学位论文,1995
[54] S.L.Ho, W.N.Fu, H.C.Wong, Application of Automatic Choice of Step Size for Time Stepping Finite Element Method to Induction Motors, IEEE Trans. on Magnetics, 1997, 33(2): 1370-1373
[55] S.L.Ho, H.L.Li, W.N.Fu, H.C.Wong, A Novel Approach to Circuit-Field-Torque Coupled Time Stepping Finite Element Modeling of Electric Machines, IEEE Trans. on Magnetics, 2000, 36(4): 1886-1889
[56] K.H.Ha, J.P.Hong, Dynamic Rotor Eccentricity Analysis by Coupling Electromagnetic and Structural Time Stepping FEM, IEEE Trans. on Magnetics, 2001, 37(5): 3452~3455
[57] G.H.Jang, J.H.Chang, Numerical analysis of the electromechanically coupled magnetic field in brushless DC motors, Journal of Magnetic Materials, 2001, 226-230(2): 1223-1225
[58] Peter N.Materu, Ramu Krishnan, Estimation of Switched Reluctance Motor Losses, IEEE Trans. on IA, 1992, 28(3): 668-679
[59] Metwally H.M.B., Faiz J., Finch J.W., Core losses in switched reluctance motor structures, ICEM 1988: 31-34
[60] 林鹤云,周鄂,黄建中等,开关磁阻电机磁场有限元分析与铁耗计算,电工技术学报,1996,11(1):24-29
[61] 吴建华,开关磁阻电机的损耗计算,微特电机,1996(2):20-22
[62] 吴建华,开关磁阻电机的设计理论及损耗计算的研究,华中理工大学博士学位论文,1994
[63] 吴恒颛,电机常用材料手册,西安:陕西科学技术出版社,2001
[64] 吴建华,詹琼华,林金铭,开关磁阻电动机的机械损耗测量,微特电机,1994(4):28-30
[65] Derrick E. Cameron, Jeffrey H. Lang, Stephen D. Umans, The origin and reduction of acoustic noise in doubly salient variable-reluctance motors, IEEE Trans. on Industry Application, 1992, 28(6): 1250-1255
[66] C.Y.Wu, C.Pollock, Time Domain Analysis of Vibration and Acoustic Noise in the Switched Reluctance Drive, Sixth international Conference on Electrical Machines and Drives, 1993: 558-563
[67] C.Y. Wu, C. Pollock, Analysis and reduction of vibration and acoustic noise in the switched reluctance drive, IEEE Trans. on Industry Application, 1995, 31(1): 91-98
[68] M.N. Anwar, Iqbal Husain, Radial force calculation and acoustic noise prediction in switched reluctance machines, IEEE Industry Applications Conference 1999: 2242-2249
[69] B.Fahimi, M.Ehsani, Spatial Distribution of Acoustic Noise Caused by Radial Vibration in Switched Reluctance Motors:Application to Design and Control, IEEE Industry Applications Conference 2000: 114-117
[70] Joon-Ho Lee,Young-Hwan Lee, Dong-Hun Kin, Ki-Sik Lee, Il-Han Park, Dynamic Vibration Analysis of Switched Reluctance Motor Using Magnetic Charge Force Density and Mechanical Analysis, IEEE Trans. on Applied Superconductivity, 2002, 12(1): 1511-1514
[71] Chenadec J.L., Torque ripple minimization in switched reluctance motors by optimisation of current waveforms and of tooth shape with copper losses and "V.A. silicon" constraints, ICEM 1994: 559-564
[72] Krzysztof Russa, Iqbal Husain, Malik E. Elbuluk, Torque-ripple minimization in switched reluctance machines over a wide speed range, IEEE Trans. on IP, 1998, 34(5): 1105-1112
[73] Sayed Mir, Malik E. Elbuluk, Iqbal Husain, Torque-ripple minimization in switched reluctance motor using adaptive fuzzy control, IEEE Trans. on IP, 1999, 35 (2): 461-468
[74] B.Fahimi, G.Suresh, K.M.Rahman, M.Ehsani, Mitigation of Acoustic Noise and Vibration in Switched Reluctance Motor Drive Using Neural Network Based Current Profiling, IEEE Industry Applications Conference 1998:715-722
[75] H. C. Lovatt, J. M. Stephenson, Computer-optimised smooth-torque current waveforms for switched-reluctance motors, IEE Proc. -Electr. Power Appl., 1997, 144(5): 310-316
[76] D. S. Schram, B. W. Williams, T. C. Green, Torque ripple reduction of switched reluctance motors by phase current optimal profiling, PESC 1992:857-860
[77] Z. Q. Zhu, S. Long, D. Howe, Significance of vibration modes in noise and vibration generation of switched reluctance motors, ICEMS 2003:672-675
[78] 于庆广,杨玉岗,开关磁阻电机(SRM)新型定子极型及其电磁关系仿真研究,系统仿真学报,2001,13(6):798-801
[79] 许家群,卞松江,杨芳春,开关磁阻电机极型改进研究,煤矿机电,2001(4):1-4
[80] 王旭东,王喜莲,开关磁阻电动机电流双幅值斩波控制,中国电机工程学报,2000,20(4):83-86
[81] 杨波,曹家勇,陈幼平,周祖德,一种降低开关磁阻电机转矩脉动的新方法,中小型电机,2001,28(4):12-16
[82] 黄建中,蒋全,周鄂,减小开关磁阻电机转矩脉动的控制策略研究,微特电机,1996(6):6-9
[83] 吴建华,陈永校,开关磁阻电机转矩波动的计算与测量,中小型电机,1997,24(2):14-16
[84] 吴建华,陈永校,开关磁阻电动机的噪声及其抑制方法,中小型电机,1997,24 (3):20-23
[85] 吴建华,陈永校,王宏华,开关磁阻电机定子固有频率的计算,中国电机工程学报,1997,17(5):326-329
[86] 王宏华,王治平,江泉,SR电机定子振动的机电类比分析,电气技术与自动化,2003(3):51-53
[87] 王宏华,陈永校,许大中,吴建华,杜军红,开关磁阻调速电机定子振动抑制,电工技术学报,1998,13(3):9-12
[88] 王宏华,王忠建,开关磁阻电动机冲击振动特性分析,中小型电机,2001年,28 (4):28-31
[89] 王宏华,对降低SR电机振动和噪声的两步换向法的实验分析,电机与控制学报,2001,5(1):32-35
[90] 王宏华,基于两步换相控制策略的SR电机直接数字控制系统设计,中国电机工程学报,2001,21(7):18-21
[91] 王忠建,王宏华,开关磁阻电动机振动特性的有限元分析,噪声与振动控制,2003(3):14-16
[92] 高明真,基于开关磁阻电机本体的噪声控制研究,中小型电机,1999,26(4):24-27
[93] 赵艳春,开关磁阻电动机的噪声及抑制方法,电气时代,2003(1):65-66
[94] J. Simkin, C. W. Trowbridge, Three-dimensional nonlinear electromagnetic field computations, using scalar potentials, IEE Proc., 1980:368-374
[95] 诸嘉慧,开关磁阻电动机电磁参数及静态特性的有限元分析,哈尔滨理工大学硕士学位论文,2003
[96] 宋志明,瞬态非线性轴对称涡流场电磁吸力的有限元解.沈阳工业大学硕士学位论文,1985
[97] 谢德馨,付继仁,邢刚,“圆盘式直流电磁铁电磁吸力的有限元解”,中小型电机,1985(1):14-16
[98] J. L. Coulomb, A methodology for the determination of global electromechanical quantities from a finite element analysis and its application to the evaluation of magnetic forces, torques and stiffness, IEEE Trans. on Mag, 1983, Mag-19(6): 2514-2518
[99] J. L. Coulomb, G. Meunier, Finite element implementation of virtual work principle for magnetic or electric force and torque computation, IEEE Trans. on Mag, 1984, Mag-20(5): 1894-1896
[100] Akihisa Kameari, Local force calculation in 3D FEM with edge elements, International J. applied electromagnetics in materials, 1993(3): 231-240
[101] Isoharu Nishiguchi, Akihisa Kameari, Kazuyoshi Haseyama, On the local force computation of deformable bodies in magnetic field, IEEE Trans. on Mag., 1999, 35(3): 1650-1653
[102] L. H. De Medeiros, G. Reyne, G. Meunier, Comparison of global force calculations on permanent magnets, IEEE Trans. on Mag, 1998, 34(5): 3560-3563
[103] Z. Ren, Comparison of Different Force Calculation Methods in 3D Finite Element Modelling, IEEE Trans. On Mag, 1994, 30(5): 3471-3474
[104] W. Muller, Comparison of different methods of force calculation, IEEE Trans. on Mag., 1990, 26(2): 1058-1061
[105] M. Ito, F. Tajima, H. Kanazawa, Evaluation of force calculating methods, IEEE Trans. on Mag., 1990, 26(2): 1035-1038
[106] T. Tarnhuvud, K. Reichert, Accuracy problems of force and torque calculation in FE-systems, IEEE Trans. on Mag., 1988, 24(1): 443-446
[107] Takefumi Kabashima, Atsushi Kawahara, Tadahiko Goto, Force calculation using magnetizing currents, IEEE Trans. on Mag., 1988, 24(1): 451-454
[108] S. J Salon, Finite Element Analysis of Electrical Machines, Kluwer Academic Publishers
[109] Mehdi Moallem, Chee-Mun Ong, Lewis E. Unnewehr, Effect of rotor profiles on the torque of a switched reluctance motor, IEEE Trans. on IP, 1992, 28(2): 364-369
[110] Alan G. Jack, John W. Finch, Julian P. Wright, Adaptive mesh generation applied to switched reluctance motor design, IEEE Trans. on IP, 1992, 28(2): 370-375
[111] O. Ichinokura, S. Suyama, T. Watanabe, H. J. Guo, A New Calculation Model of Switched Reluctance Motor for Use on Spice, IEEE Transactions on Magnetics, 2001, 37(4): 2834-2836
[112] H. C. Lovatt, J. M. Stephenson, Influence of Number of Poles Per Phase in Switched Reluctance Motors, IEE Proceedings-B, 1992, 139(4): 307-314
[113] 边敦新,郭伟,詹琼华,二维区域剖分的前处理-剖分区域的分解,电机与控制学报,2000,4(2):106-109
[114] 常国强,边敦新,詹琼华,考虑转子运动的有限元分析前处理技术,华中 理工大学学报,1998,26(6):47-49
[115] 周剑明,邵可然,周克定,异步电机场路耦合数值模拟方法,大电机技术,1995(2):28-33
[116] 杨玉岗,姚若萍,姚宏,王健,郑逢时,开关磁阻电机动态性能的研究,清华大学学报 (自然科学版),1997,37(9):82-85
[117] 郝润科,高丽云,开关磁阻电机控制方法的研究,太原理工大学学报,2000,31(2):146-151
[118] 张超,陈昊,开关磁阻电机的几种控制方案,中小型电机,2001,28(2):31-35
[119] 葛宝明,王祥珩,苏鹏声等,开关磁阻电机控制策略综述,电气传动,2001(2):8-13
[120] 王宏华,许大中,开关磁阻电动机PWM调压调速系统性能小信号分析,电工电能新技术,1997(2):9-13
[121] 王宏华,许大中,陈永校,开关型磁阻电动机脉宽调压调速系统小信号模型及调节器设计,电工技术学报,1997,12(3):1-5
[122] 刘闯,朱学忠,李磊,刘迪吉,开关磁阻发电机的脉宽调制控制,南京航空航天大学学报,2000,32(1):1-5
[123] 雷菊妹,王宏华,开关磁阻电动机电压斩波续流方式研究,中小型电机,2002,29 (6):7-9
[124] 路天航,王宏华,S R电机角度位置控制的分析与硬件仿真,电气技术与自动化,2003(1):74-76
[125] 冬雷,冯成博,开关磁阻电机相绕组匝数对性能影响的分析与设计,微特电机,2000(2):10-11
[126] 汤蕴璆,电机内的电磁场 (第二版),北京:科学出版社,1998
[127] 汤蕴璆,史乃等,电机学,西安:西安交通大学出版社,1993
[128] 冯慈璋,电磁场 (第二版),北京:高等教育出版社,1991
[129] 盛剑霓,工程电磁场数值分析,西安:西安交通大学出版社,1991
[130] 谢德馨,姚缨英,白保东,李锦彪,三维涡流场的有限元分析,北京:机械工业出版社,2000